A person purchased a used Chevrolet Cavalier for $4500. The car is expected to
decrease in value by 22% each year over
the next several years.
What would be the decay factor of a model
that would represent the value of the car?
1.22
0.78
-1.22
0.22

$1,219.5

Step-by-step explanation:

$1,219.5

Step-by-step explanation

Original price of car = $4500,

If the car depreciates by 10% after the first year

New price = 90% of 4500

New price = 0.9 * 4500

New price = £4050

Second-year

Price = 90% of 4050

Price = 0.9 * 4050

Price = $3,645

Third year:

Price = 90% * $3,645

Price = 0.9 * $3,645

Price = $3,280.5

Decrease in value = $4500 -  $3,280.5 = 1,219.5

Hence the  value of the car would have decreased by  $1,219.5 after 3 years

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}